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author | huffman |

Wed, 28 Dec 2011 13:20:46 +0100 | |

changeset 46015 | 713c1f396e33 |

parent 46014 | 2b63c77ba9c3 |

child 46016 | c42e43287b5f |

add several new tests, most of which don't work yet

--- a/src/HOL/Word/Examples/WordExamples.thy Wed Dec 28 12:55:37 2011 +0100 +++ b/src/HOL/Word/Examples/WordExamples.thy Wed Dec 28 13:20:46 2011 +0100 @@ -14,7 +14,7 @@ type_synonym word8 = "8 word" type_synonym byte = word8 --- "modulus" +text "modulus" lemma "(27 :: 4 word) = -5" by simp @@ -22,10 +22,12 @@ lemma "27 \<noteq> (11 :: 6 word)" by simp --- "signed" +text "signed" + lemma "(127 :: 6 word) = -1" by simp --- "number ring simps" +text "number ring simps" + lemma "27 + 11 = (38::'a::len word)" "27 + 11 = (6::5 word)" @@ -43,57 +45,70 @@ lemma "23 \<le> (27::8 word)" by simp lemma "\<not> 23 < (27::2 word)" by simp lemma "0 < (4::3 word)" by simp +lemma "1 < (4::3 word)" by simp +lemma "0 < (1::3 word)" by simp --- "ring operations" +text "ring operations" lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by simp --- "casting" +text "casting" lemma "uint (234567 :: 10 word) = 71" by simp lemma "uint (-234567 :: 10 word) = 953" by simp lemma "sint (234567 :: 10 word) = 71" by simp lemma "sint (-234567 :: 10 word) = -71" by simp +lemma "uint (1 :: 10 word) = 1" by simp lemma "unat (-234567 :: 10 word) = 953" by simp +lemma "unat (1 :: 10 word) = 1" by simp lemma "ucast (0b1010 :: 4 word) = (0b10 :: 2 word)" by simp lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by simp lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by simp +lemma "ucast (1 :: 4 word) = (1 :: 2 word)" by simp --- "reducing goals to nat or int and arith:" +text "reducing goals to nat or int and arith:" lemma "i < x ==> i < (i + 1 :: 'a :: len word)" by unat_arith lemma "i < x ==> i < (i + 1 :: 'a :: len word)" by uint_arith --- "bool lists" +text "bool lists" lemma "of_bl [True, False, True, True] = (0b1011::'a::len word)" by simp lemma "to_bl (0b110::4 word) = [False, True, True, False]" by simp --- "this is not exactly fast, but bearable" +text "this is not exactly fast, but bearable" lemma "of_bl (replicate 32 True) = (0xFFFFFFFF::32 word)" by simp --- "this works only for replicate n True" +text "this works only for replicate n True" lemma "of_bl (replicate 32 True) = (0xFFFFFFFF::32 word)" by (unfold mask_bl [symmetric]) (simp add: mask_def) --- "bit operations" +text "bit operations" lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by simp - lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by simp - lemma "0xF0 XOR 0xFF = (0x0F :: byte)" by simp - lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by simp +lemma "0 AND 5 = (0 :: byte)" by simp +lemma "1 AND 1 = (1 :: byte)" by simp +lemma "1 AND 0 = (0 :: byte)" by simp +lemma "1 AND 5 = (1 :: byte)" apply simp? oops +lemma "1 OR 6 = (7 :: byte)" apply simp? oops +lemma "1 OR 1 = (1 :: byte)" by simp +lemma "1 XOR 7 = (6 :: byte)" apply simp? oops +lemma "1 XOR 1 = (0 :: byte)" by simp +lemma "NOT 1 = (254 :: byte)" apply simp? oops +lemma "NOT 0 = (255 :: byte)" apply simp oops lemma "(-1 :: 32 word) = 0xFFFFFFFF" by simp lemma "(0b0010 :: 4 word) !! 1" by simp lemma "\<not> (0b0010 :: 4 word) !! 0" by simp lemma "\<not> (0b1000 :: 3 word) !! 4" by simp +lemma "\<not> (1 :: 3 word) !! 2" apply simp? oops lemma "(0b11000 :: 10 word) !! n = (n = 4 \<or> n = 3)" by (auto simp add: bin_nth_Bit0 bin_nth_Bit1) @@ -101,12 +116,18 @@ lemma "set_bit 55 7 True = (183::'a::len0 word)" by simp lemma "set_bit 0b0010 7 True = (0b10000010::'a::len0 word)" by simp lemma "set_bit 0b0010 1 False = (0::'a::len0 word)" by simp +lemma "set_bit 1 3 True = (0b1001::'a::len0 word)" apply simp? oops +lemma "set_bit 1 0 False = (0::'a::len0 word)" apply simp? oops lemma "lsb (0b0101::'a::len word)" by simp lemma "\<not> lsb (0b1000::'a::len word)" by simp +lemma "lsb (1::'a::len word)" by simp +lemma "\<not> lsb (0::'a::len word)" by simp lemma "\<not> msb (0b0101::4 word)" by simp lemma "msb (0b1000::4 word)" by simp +lemma "\<not> msb (1::4 word)" apply simp? oops +lemma "\<not> msb (0::4 word)" apply simp? oops lemma "word_cat (27::4 word) (27::8 word) = (2843::'a::len word)" by simp lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)" @@ -115,13 +136,19 @@ lemma "0b1011 << 2 = (0b101100::'a::len0 word)" by simp lemma "0b1011 >> 2 = (0b10::8 word)" by simp lemma "0b1011 >>> 2 = (0b10::8 word)" by simp +lemma "1 << 2 = (0b100::'a::len0 word)" apply simp? oops lemma "slice 3 (0b101111::6 word) = (0b101::3 word)" by simp +lemma "slice 3 (1::6 word) = (0::3 word)" apply simp? oops lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by simp lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by simp lemma "word_roti 2 0b1110 = (0b1011::4 word)" by simp lemma "word_roti -2 0b0110 = (0b1001::4 word)" by simp +lemma "word_rotr 2 0 = (0::4 word)" by simp +lemma "word_rotr 2 1 = (0b0100::4 word)" apply simp? oops +lemma "word_rotl 2 1 = (0b0100::4 word)" apply simp? oops +lemma "word_roti -2 1 = (0b0100::4 word)" apply simp? oops lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" proof -